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<Title>set_symmetric_difference</Title>
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<H1>set_symmetric_difference</H1>

<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "algorithms.gif" Alt=""   WIDTH = "194"  HEIGHT = "38" ></TD>
<TD Align=right><Img src = "function.gif" Alt=""   WIDTH = "194"  HEIGHT = "38" ></TD>
</TR>
<TR>
<TD Align=left VAlign=top><b>Category</b>: algorithms</TD>
<TD Align=right VAlign=top><b>Component type</b>: function</TD>
</TR>
</Table>

<h3>Prototype</h3>
<tt>Set_symmetric_difference</tt> is an overloaded name; there are actually two 
<tt>set_symmetric_difference</tt> functions.
<pre>
template &lt;class <A href="InputIterator.html">InputIterator</A>1, class <A href="InputIterator.html">InputIterator</A>2, class <A href="OutputIterator.html">OutputIterator</A>&gt;
OutputIterator set_symmetric_difference(InputIterator1 first1, 
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result);

template &lt;class <A href="InputIterator.html">InputIterator</A>1, class <A href="InputIterator.html">InputIterator</A>2, class <A href="OutputIterator.html">OutputIterator</A>,
          class <A href="StrictWeakOrdering.html">StrictWeakOrdering</A>&gt;
OutputIterator set_symmetric_difference(InputIterator1 first1,
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result, 
                                        StrictWeakOrdering comp);
</pre> 
<h3>Description</h3>
<tt>Set_symmetric_difference</tt> constructs a sorted range that is the set symmetric
difference of the sorted ranges <tt>[first1, last1)</tt> and <tt>[first2,
last2)</tt>.  The return value is the end of the output range.
<P>
In the simplest case, <tt>set_symmetric_difference</tt> performs a set
theoretic calculation: it constructs the union of the two sets <tt>A - B</tt>
and <tt>B - A</tt>, where <tt>A</tt> and <tt>B</tt> are the two input ranges.  That is, the
output range contains a copy of every element that is contained in
<tt>[first1, last1)</tt> but not <tt>[first2, last2)</tt>, and a copy of every element
that is contained in <tt>[first2, last2)</tt> but not <tt>[first1, last1)</tt>. 
The general case is more complicated, because the input ranges may
contain duplicate elements.  The generalization is that if a value
appears <tt>m</tt> times in <tt>[first1, last1)</tt> and <tt>n</tt> times in <tt>[first2,
last2)</tt> (where <tt>m</tt> or <tt>n</tt> may be zero), then it appears <tt>|m-n|</tt>
times in the output range.  <A href="#1">[1]</A> <tt>Set_symmetric_difference</tt> is stable, 
meaning that the relative order of elements within each input range 
is preserved.
<P>
The two versions of <tt>set_symmetric_difference</tt> differ in how they 
define whether one element is less than another.  The first version
compares objects using <tt>operator&lt;</tt>, and the second compares 
objects using a <A href="functors.html">function object</A> <tt>comp</tt>.
<h3>Definition</h3>
Defined in the standard header <A href="algorithm">algorithm</A>, and in the nonstandard
backward-compatibility header <A href="algo.h">algo.h</A>.
<h3>Requirements on types</h3>
For the first version:
<UL>
<LI>
<tt>InputIterator1</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>InputIterator2</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>OutputIterator</tt> is a model of <A href="OutputIterator.html">Output Iterator</A>.
<LI>
<tt>InputIterator1</tt> and <tt>InputIterator2</tt> have the same value type.
<LI>
<tt>InputIterator</tt>'s value type is a model of <A href="LessThanComparable.html">LessThan Comparable</A>.
<LI>
The ordering on objects of <tt>InputIterator1</tt>'s value type is a <i>strict
   weak ordering</i>, as defined in the <A href="LessThanComparable.html">LessThan Comparable</A> requirements.
<LI>
<tt>InputIterator</tt>'s value type is convertible to a type in
   <tt>OutputIterator</tt>'s set of value types.
</UL>
For the second version:
<UL>
<LI>
<tt>InputIterator1</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>InputIterator2</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>OutputIterator</tt> is a model of <A href="OutputIterator.html">Output Iterator</A>.
<LI>
<tt>StrictWeakOrdering</tt> is a model of <A href="StrictWeakOrdering.html">Strict Weak Ordering</A>.
<LI>
<tt>InputIterator1</tt> and <tt>InputIterator2</tt> have the same value type.
<LI>
<tt>InputIterator1</tt>'s value type is convertible to <tt>StrictWeakOrdering</tt>'s
   argument type.
<LI>
<tt>InputIterator</tt>'s value type is convertible to a type in
   <tt>OutputIterator</tt>'s set of value types.
</UL>
<h3>Preconditions</h3>
For the first version:
<UL>
<LI>
<tt>[first1, last1)</tt> is a valid range.
<LI>
<tt>[first2, last2)</tt> is a valid range.
<LI>
<tt>[first1, last1)</tt> is ordered in ascending order according to
   <tt>operator&lt;</tt>.  That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
   in <tt>[first1, last1)</tt> such that <tt>i</tt> precedes <tt>j</tt>, 
   <tt>*j &lt; *i</tt> is <tt>false</tt>.
<LI>
<tt>[first2, last2)</tt> is ordered in ascending order according to
   <tt>operator&lt;</tt>.  That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
   in <tt>[first2, last2)</tt> such that <tt>i</tt> precedes <tt>j</tt>, 
   <tt>*j &lt; *i</tt> is <tt>false</tt>.
<LI>
There is enough space to hold all of the elements being copied.
   More formally, the requirement is that 
   <tt>[result, result + n)</tt> is a valid range, where <tt>n</tt> is the number
   of elements in the symmetric difference of the two input ranges.
<LI>
<tt>[first1, last1)</tt> and <tt>[result, result + n)</tt> do not overlap.
<LI>
<tt>[first2, last2)</tt> and <tt>[result, result + n)</tt> do not overlap.
</UL>
For the second version:
<UL>
<LI>
<tt>[first1, last1)</tt> is a valid range.
<LI>
<tt>[first2, last2)</tt> is a valid range.
<LI>
<tt>[first1, last1)</tt> is ordered in ascending order according to
   <tt>comp</tt>.  That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
   in <tt>[first1, last1)</tt> such that <tt>i</tt> precedes <tt>j</tt>, 
   <tt>comp(*j, *i)</tt> is <tt>false</tt>.
<LI>
<tt>[first2, last2)</tt> is ordered in ascending order according to
   <tt>comp</tt>.  That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
   in <tt>[first2, last2)</tt> such that <tt>i</tt> precedes <tt>j</tt>, 
   <tt>comp(*j, *i)</tt> is <tt>false</tt>.
<LI>
There is enough space to hold all of the elements being copied.
   More formally, the requirement is that 
   <tt>[result, result + n)</tt> is a valid range, where <tt>n</tt> is the number
   of elements in the symmetric difference of the two input ranges.
<LI>
<tt>[first1, last1)</tt> and <tt>[result, result + n)</tt> do not overlap.
<LI>
<tt>[first2, last2)</tt> and <tt>[result, result + n)</tt> do not overlap.
</UL>
<h3>Complexity</h3>
Linear.  Zero comparisons if either <tt>[first1, last1)</tt> or <tt>[first2, last2)</tt>
is empty, otherwise at most <tt>2 * ((last1 - first1) + (last2 - first2))
- 1</tt> comparisons.
<h3>Example</h3>
<pre>
inline bool lt_nocase(char c1, char c2) { return tolower(c1) &lt; tolower(c2); }

int main()
{
  int A1[] = {1, 3, 5, 7, 9, 11};
  int A2[] = {1, 1, 2, 3, 5, 8, 13};  
  char A3[] = {'a', 'b', 'b', 'B', 'B', 'f', 'g', 'h', 'H'};
  char A4[] = {'A', 'B', 'B', 'C', 'D', 'F', 'F', 'H' };

  const int N1 = sizeof(A1) / sizeof(int);
  const int N2 = sizeof(A2) / sizeof(int); 
  const int N3 = sizeof(A3);
  const int N4 = sizeof(A4);

  cout &lt;&lt; &quot;Symmetric difference of A1 and A2: &quot;;
  set_symmetric_difference(A1, A1 + N1, A2, A2 + N2,
                           ostream_iterator&lt;int&gt;(cout, &quot; &quot;));
  cout &lt;&lt; endl 
       &lt;&lt; &quot;Symmetric difference of A3 and A4: &quot;;
  set_symmetric_difference(A3, A3 + N3, A4, A4 + N4, 
                           ostream_iterator&lt;char&gt;(cout, &quot; &quot;),
                           lt_nocase);
  cout &lt;&lt; endl;
}
</pre>
<P>
The output is
<pre>
Symmetric difference of A1 and A2: 1 2 7 8 9 11 13 
Symmetric difference of A3 and A4: B B C D F g H 
</pre>
<h3>Notes</h3>
<P><A name="1">[1]</A>
Even this is not a completely precise description, because
the ordering by which the input ranges are sorted
is permitted to be a strict weak ordering that is not a total ordering:
there might be
values <tt>x</tt> and <tt>y</tt> that are equivalent (that is, neither <tt>x &lt; y</tt> nor
<tt>y &lt; x</tt>) but not equal.  See the <A href="LessThanComparable.html">LessThan Comparable</A>
requirements for a more complete discussion. The output range consists of
those elements from <tt>[first1, last1)</tt> for which equivalent elements do
not exist in <tt>[first2, last2)</tt>, and 
those elements from <tt>[first2, last2)</tt> for which equivalent elements do
not exist in <tt>[first1, last1)</tt>.
Specifically, suppose that the range
<tt>[first1, last1)</tt> contains <tt>m</tt> elements that are equivalent to each
other and the range <tt>[first2, last2)</tt> contains <tt>n</tt> elements from that
equivalence class (where either <tt>m</tt> or <tt>n</tt> may be zero).  If <tt>m &gt; n</tt>
then the output range contains the <i>last</i> <tt>m - n</tt> of these
elements elements from <tt>[first1, last1)</tt>, and if <tt>m &lt; n</tt> then the
output range contains the last <tt>n - m</tt> of these elements elements
from <tt>[first2, last2)</tt>.
<h3>See also</h3>
<tt><A href="includes.html">includes</A></tt>, <tt><A href="set_union.html">set_union</A></tt>, <tt><A href="set_intersection.html">set_intersection</A></tt>, 
<tt><A href="set_difference.html">set_difference</A></tt>, <tt><A href="sort.html">sort</A></tt>

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